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Bergman Complex of a Matroid
Algebra & Discrete Mathematics| Speaker: | Carly Klivans, MSRI |
| Location: | 693 Kerr |
| Start time: | Fri, Oct 31 2003, 2:10PM |
Description
The Bergman complex was first defined as the logarithmic limit
set of an algebraic variety. More recently, it has appeared in the thoery
of tropical geometry. In a special case, the complex can be reformulated
in terms of matroids. We show that the Bergman complex of a matroid is
the order complex of the lattice of flats of the matroid. Moreover, we
show that for graphical matroids of complete graphs, the Bergman complex
is the space of phylogentic trees.